Question: Simplify the following expression: $\dfrac{30t}{18t^4}$ You can assume $t \neq 0$.
Explanation: $ \dfrac{30t}{18t^4} = \dfrac{30}{18} \cdot \dfrac{t}{t^4} $ To simplify $\frac{30}{18}$ , find the greatest common factor (GCD) of $30$ and $18$ $30 = 2 \cdot 3 \cdot 5$ $18 = 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(30, 18) = 2 \cdot 3 = 6 $ $ \dfrac{30}{18} \cdot \dfrac{t}{t^4} = \dfrac{6 \cdot 5}{6 \cdot 3} \cdot \dfrac{t}{t^4} $ $\phantom{ \dfrac{30}{18} \cdot \dfrac{1}{4}} = \dfrac{5}{3} \cdot \dfrac{t}{t^4} $ $ \dfrac{t}{t^4} = \dfrac{t}{t \cdot t \cdot t \cdot t} = \dfrac{1}{t^3} $ $ \dfrac{5}{3} \cdot \dfrac{1}{t^3} = \dfrac{5}{3t^3} $